Grade 6 Math Curriculum Alignment With State Standards

Grade 6 Math Curriculum Alignment with State Standards NM Statute 22-13-1.6.A. Each school district shall align its curricula to meet the state standards for each grade level and subject area so that students who transfer between public schools within the school district receive the same educational opportunity within the same grade or subject area.

District: Textbook: Holt Math Course 1

5-8 Benchmark N.1: Understand numbers, ways of Strand: NUMBER AND Standard: Students will understand numerical representing numbers, relationships among numbers, and OPERATIONS concepts and mathematical operations. number systems.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.N.1.1 Compare and order rational 181-182, 185-186, 192-193, 198-200 numbers. 6.N.1.2 Use equivalent 106, 186-188, 352-353, 356-357, 360, 380-382, 385- representations for rational numbers 389 (e.g., integers, decimals, fractions, percents, ratios, numbers with whole-number exponents). 6.N.1.3 Use appropriate 181-184, 189, 192, 194-195, 199 representations of positive rational numbers in the context of real-life applications. 6.N.1.4 Identify greatest common 173-176, 177, 228-231 factor and least common multiples for a set of whole numbers. 6.N.1.5 Identify and represent on a 181-182, 602-603, 606-607 number line decimals, fractions, mixed numbers, and positive and negative integers.

Grade 6 Math Curriculum Alignment with State Standards

Strand: NUMBER AND Standard: Students will understand numerical 5-8 Benchmark N.2: Understand the meaning of operations OPERATIONS concepts and mathematical operations. and how they relate to one another.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.N.2.1 Calculate multiplication and 24-25, 57, 71, 130-133, 135-136, 138-140, 253, 255, division problems using contextual 262, 263, 272 situations. 6.N.2.2 Factor a whole number into 169-172 a product of its primes. 6.N.2.3 Demonstrate the 352-353, 356-357, 360-361, 380-382, 386, 389 relationship and equivalency among ratios and percents. 6.N.2.4 Use proportions to solve 362-365 problems. 6.N.2.5 Explain and perform: 19, 22-26, 116-121, 128-133, 137-138, 232-233, 234- a. whole number division and 237, 242-247 express remainders as decimals or appropriately in the context of the problem b. addition, subtraction, multiplication, and division with decimals c. addition and subtraction with integers d. addition, subtraction, and multiplication with fractions and mixed numerals 6.N.2.6 Determine the least 173-177, 228-231, 232-233 common multiple and the greatest common divisor of whole numbers and use them to solve problems with fractions.

Strand: NUMBER AND Standard: Students will understand numerical 5-8 Benchmark N.3: Compute fluently and make OPERATIONS concepts and mathematical operations. reasonable estimates.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.N.3.1 Estimate quantities 10-13, 206-209 involving rational numbers using various estimations. 6.N.3.2 Use estimates to check 10-13, 56, 72, 112-115, 206-209, 499, 687 reasonableness of results and make predictions in situations involving rational numbers. 6.N.3.3 Determine if a problem 10-13, 30-32, 379 situation calls for an exact or approximate answer and perform the appropriate computation. 6.N.3.4 Compare and order positive 108-109, 198-199, 606-607 and negative fractions, decimals, and mixed numbers and place them on a number line. 6.N.3.5 Convert fractions to 181-184, 381-384, 385-388, 389 decimals and percents and use these representations in estimations, computations, and applications. 6.N.3.6 Interpret and use ratios in 352-355, 356-359, 360-361 different contexts. 6.N.3.7 Compute and perform 128-129, 130-133, 134-136, 137-143, 260-263, 264- multiplication and division of 267, 268-269, 270-273 fractions and decimals and apply these procedures to solving problems.

5-8 Benchmark A.1: Understand patterns, relations, and Strand: ALGEBRA Standard: Students will understand algebraic concepts and applications. functions.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.A.1.1 Solve problems involving 362-365, 366-369, 370-372, 373, 374-377, 390-393, proportional relationships. 394-397, 399 6.A.1.2 Graph ordered pairs in the 319-321, 610-614 coordinate plane. 6.A.1.3 Explain and use symbols to 54-57, 58-61, 62-65, 69, 75, 77, 80, 82 represent unknown quantities and variable relationships. 6.A.1.4 Explain and use the 352-353, 356-357, 360-361, 362-365, 380-388 relationships among ratios, proportions, and percents. 6.A.1.5 Make generalizations 15, 33-36, 37, 450-453, 506 based on observed patterns and relationships.

Standard: Students will understand algebraic 5-8 Benchmark A.2: Represent and analyze mathematical Strand: ALGEBRA concepts and applications. situations and structures using algebraic symbols.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.A.2.1 Solve problems involving 362-365, 366-369, 370-372, 373, 374-377, 390-393, proportional relationships. 394-397, 399 6.A.2.2 Use letters to represent an 54-57, 58-61, 62-65, 69, 70-73, 75, 77, 80, 82 unknown in an equation. 6.A.2.3 Solve one-step linear 70-73, 74-77, 78-80, 85-86, 90-91, 144-147 equations and inequalities in one variable with positive whole-number solutions. 6.A.2.4 Demonstrate that a variable 54-55, 640-641 can represent a single quantity that changes. 6.A.2.5 Demonstrate how changes 644-649 in one variable affect other variables.

Standard: Students will understand algebraic 5-8 Benchmark A.3: Use mathematical models to represent Strand: ALGEBRA concepts and applications. and understand quantitative relationships.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.A.3.1 Develop and use 66-67, 106-107, 185, 232-233, 258-259, 268-269, 380, mathematical models to represent 616, 621, 634-635 and justify mathematical TE 75, 199, 235, 265, 357, 438, 451, 515, 577, relationships found in a variety of 583, 647 situations. 6.A.3.2 Create, explain, and use 18-20, 70-77, 90-92, 212-213, 294-295, 308-311, 312- mathematical models such as: 313, 580-581 a. Venn diagrams to show the relationships between the characteristics of two or more sets b. equations and inequalities to model numerical relationships c. three-dimensional geometric models d. graphs, tables, and charts to interpret and analyze data

Standard: Students will understand algebraic Strand: ALGEBRA 5-8 Benchmark A.4: Analyze changes in various contexts. concepts and applications.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.A.4.1 Represent and explain 54, 70-73, 77, 80, 86 changes using one-step equations with one variable. 6.A.4.2 Solve problems that involve 362-365, 366-369, 370-372, 373, 374-377, 390-393, change using proportional 394-397, 399 relationships. 6.A.4.3 Use ratios to predict 352-355 changes in proportional situations. 6.A.4.4 Use tables and symbols to 33-36, 66-67, 356-359, 496-499, 500-503, 504-507 represent and describe proportional and other relationships involving conversions, sequences, and perimeter. 6.A.4.5 Generate formulas to 66-67, 554-556 represent relationships involving changes in perimeter.

5-8 Benchmark G.1: Analyze characteristics and properties Standard: Students will understand geometric of two- and three-dimensional geometric shapes and Strand: GEOMETRY concepts and applications. develop mathematics arguments about geometric relationships.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.G.1.1 Identify, describe, and 420-423, 427, 428-431, 432-433, 436, 437-440, 441, classify the properties of, and the 442-445, 447, 564-565 relationships between, plane and solid geometric figures: a. measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software) b. understand that the sum of angles of any triangle is 180 degrees and the sum of the angles of any quadrilateral is 360 degrees and use this information to solve problems c. visualize and draw two- dimensional views of three- dimensional objects made from rectangular solids 6.G.1.2 Classify angles as right, 420-422 obtuse, or straight. 6.G.1.3 Describe the properties of 446, 520-521, 566-567, 764 geometric figures that include regular polygons, circles, ellipses, cylinders, cones, spheres, and cubes. 6.G.1.4 Classify polygons as 446-449 regular or irregular. 6.G.1.5 Classify triangles as 436-438 scalene, isosceles, or equilateral and by angles (i.e., right, acute, and obtuse). Page 8 6.G.1.6 Identify angle, line, 416-418 segment, and ray and use the symbols for each. 6.G.1.7 Describe the relationship 518-521 between radius, diameter, and circumference of a circle.

5-8 Benchmark G.2: Specify locations and describe spatial Standard: Students will understand geometric Strand: GEOMETRY relationships using coordinate geometry and other concepts and applications. representational systems.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.G.2.1 Use coordinate geometry to 463 describe location on a plane. 6.G.2.2 Recognize skewed lines in 428-430 space.

Standard: Students will understand geometric 5-8 Benchmark G.3: Apply transformations and use Strand: GEOMETRY concepts and applications. symmetry to analyze mathematical situations.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.G.3.1 Identify line of symmetry 446-465 with rotation and scaling.

Standard: Students will understand geometric 5-8 Benchmark G.4: Use visualization, spatial reasoning, Strand: GEOMETRY concepts and applications. and geometric modeling to solve problems.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.G.4.1 Use appropriate 436, 441, 463, 518-519, 550, 557, 564-565, 580-581 technology, manipulatives, constructions, or drawings to recognize or compare geometric figures.

5-8 Benchmark M.1: Understand measurable attributes of Standard: Students will understand measurement Strand: MEASUREMENT objects and the units, systems, and processes of systems and applications. measurement.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.M.1.1 Perform multi-step 496-499, 500-503, 504-507 conversions of measurement units to equivalent units within a given system (e.g., 36 inches equals 3 feet or 1 yard). 6.M.1.2 Estimate measurement in 488-490, 492-495 both U.S. customary and metric units. 6.M.1.3 Select and use units of 420, 486-489 appropriate size and type to measure angles (e.g., degrees, radians), perimeter, area, and capacity in both U.S. customary and metric systems. 6.M.1.4 Use standard units of linear 486 measurement to the nearest sixteenth of an inch; metric measurements to the nearest millimeter.

Standard: Students will understand measurement 5-8 Benchmark M.2: Apply appropriate techniques, tools, Strand: MEASUREMENT systems and applications. and formulas to determine measurements.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.M.2.1 Apply various 486-489, 492-493, 504-505 measurement techniques and tools, units of measure, and degrees of accuracy to find accurate rational number representations for length, liquid, weight, perimeter, temperature, and time. 6.M.2.2 Select and use formulas for 514-516 perimeters of squares and rectangles. 6.M.2.3 Select and use strategies 420-423, 488-489, 490-491, 492, 493, 494, 495 to estimate measurements including angle measure and capacity. 6.M.2.4 Select and justify the 486-491, 492-495 selection of measurement tools, units of measure, and degrees of accuracy appropriate to the given situation.

Standard: Students will understand how to 5-8 Benchmark D.1: Formulate questions that can be Strand: DATA ANALYSIS AND formulate questions, analyze data, and determine addressed with data and collect, organize, and display PROBABILITY probabilities. relevant data to answer them.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.D.1.1 Use statistical 294-296, 300, 302-305, 308-311, 312-313, 314-317, representations to analyze data. 337 6.D.1.2 Draw and compare different 309, 315, 316, 323, 326-329, 333-335 graphical representations of the same data. 6.D.1.3 Use mean, median, mode, 298-301, 302-305 and range to describe data. 6.D.1.4 Sketch circle graphs to 524-525 display data. 6.D.1.5 Solve problems by 294-296, 297, 302-305, 308-311, 337, 347 collecting, organizing, displaying and interpreting data. 6.D.1.6 Compare different samples 318 of a population with the entire population and determine the appropriateness of using a sample. 6.D.1.7 Conduct and explain 318 sampling techniques such as observations, surveys, and random sampling for gathering data. 6.D.1.8 Determine the median for a 299 rational number data set containing an odd number of data points. 6.D.1.9 Calculate and explain the 299, 300 median for a whole number data set containing an even number of data points. 6.D.1.10 Explain advantages and 326-329, 333-335 disadvantages of using various display formats for a specific data set.

6.D.1.11 Formulate and solve 294-296, 308-311, 314-318 problems by collecting, organizing, displaying, and interpreting data.

Standard: Students will understand how to Strand: DATA ANALYSIS AND 5-8 Benchmark D.2: Select and use appropriate statistical formulate questions, analyze data, and determine PROBABILITY methods to analyze data. probabilities.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.D.2.1 Choose an appropriate 333-335 graphical format to organize and represent data. 6.D.2.2 Describe the effects of 302-305, 326-329 missing or incorrect data. 6.D.2.3 Compute and analyze 297-299, 302-305 statistical measurements for data sets: a. understand how additional data added to data sets may affect the computations of central tendency b. understand how the inclusion or exclusion of outliers affects measures of central tendency c. know why a specific measure of central tendency provides the most useful information in a given context 6.D.2.4 Use data samples of a 318 population and describe the characteristics and limitations of the sample. 6.D.2.5 Identify different ways of Please see Hands-On Lab Activities pp. 171-174 selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population. 6.D.2.6 Explain how the way a 318 question is asked in a survey might influence the results obtained.

6.D.2.7 Identify data that represent Please see Hands-On Lab Activities pp. 171-174 sampling errors and explain why the sample and the display might be biased. 6.D.2.8 Identify claims based on 326-329 statistical data and, in sample cases, evaluate the validity and usefulness of the claims.

Standard: Students will understand how to Strand: DATA ANALYSIS AND 5-8 Benchmark D.3: Develop and evaluate inferences and formulate questions, analyze data, and determine PROBABILITY predictions that are based on data. probabilities.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.D.3.1 Identify claims based on 326-329 statistical data and evaluate the validity of the claim 6.D.3.2 Conduct observations, 318, 676-677, 694-697 surveys, experiments and/or simulations, record the results in charts, tables, or graphs, and use the results to draw conclusions and make predictions. 6.D.3.3 Find all possible 692-693 combinations in a given set (e.g., the number of ways a set of books can be arranged on a shelf). 6.D.3.4 Compare expected results 672-677 with actual results in a simple experiment.

Standard: Students will understand how to Strand: DATA ANALYSIS AND 5-8 Benchmark D.4: Understand and apply basic concepts formulate questions, analyze data, and determine PROBABILITY of probability. probabilities.

Grade 6 Performance Standards Grade 6 Textbook Pages Supplemental Materials Month(s) when Addressed 6.D.4.1 List all possible outcomes 688-691 for a compound event composed of two independent events and recognize whether an outcome is certain, impossible, likely, or unlikely. 6.D.4.2 Determine and compare 672-675, 682-685 experimental (empirical) and mathematical (theoretical) probabilities (e.g., flipping two color counters). 6.D.4.3 Determine theoretical and 672-675, 682-685 experimental probabilities and use them to make predictions about events. 6.D.4.4 Represent all possible 688-691 outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome. 6.D.4.5 Use data to estimate the 694-697 probability of future events (e.g., batting averages). 6.D.4.6 Represent probabilities as 682-685 ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of the event not occurring. Page 20 6.D.4.7 Describe the difference 700-701 between independent and dependent events and identify situations involving independent or dependent events.